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6 – MERTIS SHORT TERM SHUTTER DEMONSTRATOR MODEL Coil Dimension Figure 6.2: Helmholtz VCA dimension parameters shown in the axisymmetric cross section. hC n = d Boundary Conditions l S L = 9mm R = 3mm l m = d N = 1. 3mm ζ = 0. 1mm tot L = 2δ + 2l R = r δ = 0. 25mm ε = 0. 15mm D C = 2 mn M D C + l + ε + h C S + ζ ( dueoptimization) ( adjustment clearance) ( boundary condition) ( boundary condition) ( gluethickness) ( magnet clearance) Coil wire diameter dD with insulation and copper thickness of 0.15mm. 1. single coating 2. double coating fine Figure 6.3: Photo of the MSTS DM. 3. double coating thick No. dD / mm ⎣n⎦ ⎡m⎤ Ntot Rtot / Ω Imax / mA Fmax / mN P / W 1 0.164 10 22 440 5.46 495 127.9 1.34 2 0.174 10 21 420 5.21 518 127.8 1.4 3 0.185 9 20 360 4.47 604 127.7 1.63 Comments lC NdFeB d lM • UC=2.7V as maximum output voltage of an applicable H-bridge amplifier. • Increasing the wire thickness lowers the resistance, thus increases the force and, however, the dissipated power. lC ζ hC χ 2 50

6 – MERTIS SHORT TERM SHUTTER DEMONSTRATOR MODEL Parameter Value fres 109.1 Hz m 194.6 mg c 91.46 Nm−1 k 1.652 · 10−3 kgs−1 RC 1.712 Ω L 38 µH Table 6.3: Measured mechanical and electromagnetic parameters of the MSTS DM. Note that the spring constant c was not measured for the MSTS DM, but was deduced from the step response and, therefore, slightly differs to the value listed in table 6.1 design of the control electronics. Since the MSTS builds a electromechanical system, the calculated parameters resulting from the separated considerations discussed in the previous sections must slightly differ to the measured parameters. Table 6.3 lists the measured parameters of the MSTS DM. 6.4.1 Static Measurement The spring constant can be determined by a force measurement at static deflections. Figure 6.4 shows the resulting linear characteristic of the MSTS FH structure, whereas its slope corresponds to the spring constant, which can be calculated to c = 82.3 Nm −1 . This value almost coincides with the simulated value (tab. 6.1). Thus, it can be con- cluded, that the leafs of MSTS FH structure were accurately cut by the manufacturer. 6.4.2 Dynamic Measurement Figure 6.5 shows the measured step response of the MSTS DM VCA excited by a symmetric rectangular signal with f = 0.9 Hz. Due to the weak damping ratio D, the highest peak reaches almost the double value of the steady state amplitude. The sys- tem’s resonant frequency can be determined to fres= 109.1 Hz. With (4.11) to (4.13), the attenuation constant can be calculated to k = 1.652·10 −3 kgs −1 . When considering this measurement result, it becomes obvious, that the MSTS control electronics must be very well adjusted to reach the required open/close time. The spring mass can be calculated with (4.10) to m = 194.6 mg considering the mea- sured spring constant c and the attenuation constant k. These values will be used to define the experimental model of the control path. 51

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